The Biinvariant Diagonal Class for Hamiltonian Torus Actions

Content Provider	Semantic Scholar
Author	Mundet, Ignasi Canales Riera, Inmaculada Vilardell I
Copyright Year	2006
Abstract	Suppose that an algebraic torus G acts algebraically on a projective man-ifold X with generically trivial stabilizers. Then the Zariski closure of the set of pairs {(x, y) ∈ X × X | y = gx for some g ∈ G} defines a nonzero equivariant cohomology class [∆ G ] ∈ H * G×G (X × X). We give an analogue of this construction in the case where X is a compact symplectic manifold endowed with a hamiltonian action of a torus, whose complexification plays the role of G. We also prove that the Kirwan map sends the class [∆ G ] to the class of the diagonal in each symplectic quotient. This allows to define a canonical right inverse of the Kirwan map.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://arxiv.org/pdf/math/0412218v2.pdf
Language	English
Access Restriction	Open
Subject Keyword	Analog Closure Delta operator Difference quotient Hamiltonian (quantum mechanics) Linear algebra SMO wt Allele Symplectic integrator manifold
Content Type	Text
Resource Type	Article